On the Osofsky-smith Theorem
نویسندگان
چکیده
We recall a version of the Osofsky-Smith theorem in the context of a Grothendieck category and derive several consequences of this result. For example, it is deduced that every locally finitely generated Grothendieck category with a family of completely injective finitely generated generators is semisimple. We also discuss the torsion-theoretic version of the classical Osofsky theorem which characterizes semisimple rings as those ring whose every cyclic module is injective.
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